Can you describe the steps that you are taking to import the converted clips into iMovie, and what happens when you try? Any error message?
iMovie will recognize Mp4/AAC. Specifically, it recognizes the Handbrake conversion to that format. Open one of the converted clips in QuickTimePlayer, and do a Window/Show Movie Inspector. What video and audio format are shown?
A few quick things that you can do is to reboot your Mac. Create a new iMovie project and import into the new project.
If no luck, try deleting preferences. To delete/reset preferences, open iMovie while holding down the Option and Command keys and select to delete preferences in the box that appears. iMovie will open in a new empty library. Reopen your old library to get back to your projects. Possibly you may need to reboot to set the changes. Deleting preferences is a safe procedure that will not cause data loss or disruption to your project.
Failing that, try opening iMovie in a new library. To do that, open iMovie while holding down the Option key and then selecting to create a new library in the box that appears.
Finally, you can try opening iMovie in a new user account. The guest account on your Mac would serve for that.
-- Rich